1. Field of the Invention
The present invention relates to a technique for manufacturing an exposure mask for use in a light or X-ray exposure method and more particularly, the present invention relates to a calculation method, a verification method, a verification program, a verification system, and a semiconductor device manufacturing method, for an edge deviation quantity of a finish pattern from a desired pattern in order to obtain a fine pattern.
2. Description of the Related Art
Advancement of a semiconductor manufacturing technique in recent years is very remarkable, and a semiconductor device such as LSI whose size is 0.18 μm in minimum design rule is mass-produced. Such a fine LSI is achieved by remarkable advance of a fine pattern forming techniques such as a mask process technique, a photolithography technique, and an etching technique.
In an age in which a pattern size is large, an LSI pattern to be formed on a wafer is depicted as a design pattern as is; a mask pattern which is faithful to the design pattern is produced; the mask pattern is transferred onto the wafer by means of a projection optical system; and a target layer is etched, whereby a pattern which is almost identical to the design pattern can be formed on the wafer. However, with advancement of fine patterning, it becomes difficult to faithfully form a pattern in each process. Thus, there occurs a problem that the finish pattern is not provided as the desired pattern.
With respect to how patterns are called, such patterns are discriminated from one another as follows. A pattern desired as an LSI in view of device features, wiring characteristics or the like is referred to as a “desired pattern”, a pattern obtained by designing a pattern as close to the desired pattern as possible is referred to as a “design pattern”, and a pattern to be formed on a wafer, which is predicted from the design pattern, is referred to as a “finish pattern”.
In particular, in lithography and an etching process which are the most important to achieve fine processing, another pattern layout environment allocated in a peripheral region of a region for forming a pattern is greatly influenced on dimensional precision of the pattern. As a technique for reducing the influence, there has been reported a correction technique such as a technique for Optical Proximity Correction (hereinafter, simply referred to as OPC) or a technique for Process Proximity Correction (hereinafter, simply referred to as PPC) in which an auxiliary pattern is added in advance in a design pattern such that a finish pattern is close to the desired pattern.
However, with complication of the OPC and PPC techniques in recent years, a pattern produced by a device designer and a mask pattern for use during exposure are greatly different from each other, and thus, a finish pattern to be formed on a wafer cannot be easily predicted. Therefore, in the case where a desired pattern cannot be obtained as a result of simulation after the finish pattern has been predicted by using an OPC tool and a lithography simulator, a design technique is employed for correcting a design pattern. In such a design technique, it is required that an edge deviation quantity indicating a deviation between a design pattern and a finish pattern is calculated within a short period of time.
There has been proposed that the edge deviation quantity is calculated by computing a light beam intensity using a Hopkins's Formula (U.S. Pat. No. 6,470,489 (page 20). A conventional method of calculating an edge deviation quantity based on the Hopkins Formula will be described with reference to FIGS. 13 to 15.
FIG. 13 schematically shows a desired pattern 41 and a design pattern 42 with respect to a method of calculating an edge deviation quantity, and also schematically shows a light beam intensity obtained from the design pattern 42. These patterns are depicted to correspond to a position coordinate shown in FIG. 13. FIG. 14 is a flow chart showing an outline of procedures for obtaining an edge deviation quantity. FIG. 15 is a flow chart showing calculation procedures in the Hopkins Formula in steps S54 and S55.
First, in designing an LSI or the like, the desired pattern 41 required to ensure device characteristics and the design pattern 42 to achieve the desired pattern 41 are produced (step S51). The design pattern 42 is not applied with OPC or the like.
Next, an exposure reference light beam intensity (Ith) for forming the design pattern 42 on a wafer is set (step S52).
Then, in order to make a comparison of a finish pattern obtained by calculation based on the design pattern 42 with the desired pattern 41, a plurality of evaluation points, for example, two evaluation points, i.e., an evaluation point 51 indicating an edge position of the desired pattern 41 and an evaluation point 52 in the vicinity of the evaluation point 51, are set on a light beam intensity characteristic curve (step S53).
Then, a light beam intensity I(t5) in the evaluation point 51 (position coordinate t5) of an edge position of the desired pattern 41 is calculated from the Hopkins Formula described later (step S54).
Next, a light beam intensity I(t6) in a position coordinate t6 of the evaluation point 52 which is slightly displaced from the position coordinate t5 is calculated from the Hopkins Formula (step S55).
Here, in the above steps S54 and S55, a partial coherent image forming Formula of Hoplkins for use in calculation of a light beam intensity is expressed as follows.
                              I          ⁡                      (            t            )                          =                                  ⁢                  ∫                                    ∫                              -                ∞                            ∞                        ⁢                                          TCC                ⁡                                  (                                      ω                    ,                                                                                  ⁢                                          ω                      ′                                                        )                                            ×                                                          ⁢                              M                (                                                                  ⁢                ω                )                            ×                                                          ⁢                                                M                  ⁡                                      (                                          ω                      ′                                        )                                                  *                            ×                                                                                        ⁢                              exp            ⁡                          (                                                ⅈ                  ⁡                                      (                                          ω                      -                                              ω                        ′                                                              )                                                  ⁢                t                            )                                ⁢                      ⅆ            ω                    ⁢                      ⅆ                          ω              ′                                          
In Formula (1), TCC denotes a Transmission Cross Coefficient; I(t) denotes a light beam intensity in a position coordinate “t”; M denotes a Fourier transform of a mask complex transmission rate distribution in a frequency plane; M* denotes a complex conjugate of the Fourier transform of the mask complex transmission distribution in the frequency plane; “i” denotes an imaginary unit; and ω and ω ′denote angular frequencies.
Now, calculation procedures of Formula (1) will be described with reference to a flow chart of FIG. 15.
First, calculation of TCC(ω, ω′) is carried out (step S61).
Subsequently, M(ω), the Fourier transform of complex amplitude transmission distribution of the design pattern is carried out, and M(ω′) is determined (step S62).
Next, a product of the calculated results in steps S61 and S62, which expressed by TCC(ω, ω′)×M(ω′)×M(ω′), is calculated (step S63).
Then, a product of the formula in step S63 and exp(i(ω−ω′)t) which is the reverse Fourier transform in step S63 is integrated with respect to ω, ω′ (step S64).
As has been described above, by the above-described Hopkins Formula of Formula (1), light beam intensity I(t5), I(t6) of the position coordinate t5, t6 Of the evaluation points 51 and 52 are calculated, and a Formula of a straight line 53 connecting the light beam intensity I(t5), I(t6) of the position coordinate t5, t6 of these evaluation points 51 and 52 is calculated (step S56).
Next, from this straight line 53, a position coordinate t7 of an intersection 54 at which the light beam intensity becomes a reference light beam intensity (Ith) is calculated (step S57).
Then, a difference between the position coordinate t5 and the position coordinate t7 is calculated, and this difference is defined as an edge deviation quantity 56 (step S58).
In this manner, it is quantitatively determined how large the finish pattern calculated from the design pattern 42 is deviated from the desired pattern 41.
In the above-described conventional method of calculating an edge deviation quantity, the light beam intensities in the position coordinates t5 and t6 of the two evaluation points 51 and 52 are calculated by the above-described Hopkins Formula. In this case, it is required to calculate the reverse Fourier transform of an angular frequency distribution at each of the position coordinates. In particular, calculation of a trigonometric function (cos(ω−ω′)t−i sin(ω−ω′)t) expanding a portion of exp(i(ω−ω′)t) on which a great calculation load is applied is carried out two times. Thus, there has been a problem that much time is required for calculation of the trigonometric function, and an edge deviation quantity cannot be calculated with high precision for a short period of time.